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I was asked the following puzzle for an interview.

There is a square sheet. A smaller square hole is made on it (at a random place). How can I divide the rest of the sheet into two halves (in terms of the total area)?

How to solve this?

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up vote 11 down vote accepted

Draw a line joining the centers of the two squares and cut along that line.

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Works even if the two squares do not have parallel sides :-) – Henning Makholm Mar 5 '12 at 3:21
This also works for any figures for which there is a point such that all lines through the point divide the figure into two parts of equal area. The figures do not have to be the same shape, only that each has such a point and the line is drawn between the points. If the points coincide, any line through it will do. – marty cohen Mar 5 '12 at 5:46
And for n dimensions, take n objects each with a point such that any n-1 dimensional hyperplane divides it into two n-dimensional parts of equal n-dimensional volume. Then the n-1 dimensional hyperplane through these n centers divide each object and threfore the "holed" object into two parts of equal volume. – marty cohen Mar 5 '12 at 5:51

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